The slope of a perpendicular line is its opposite reciprocal
So in this case, the perpendicular line for y=2x+8 is y=-1/2x+8
But we are looking for a different y-intercept since the equation has to pass through (6,-6), so we have -6=-1/2(6)+b and we can solve for b:
-6=-1/2(6)+b
-6=-3+b
-3=b
So the equation for line k is y=-1/2x-3
Hope this helped. Comment below if you'd like me to clarify anything.
